[DIYbio] Can I use EcoRI and NheI in Saccharomyces cerevisiae

Hi all

It seems like kind of a stupid question to myself, but I am somewhat stuck at the moment. I aim to cut a specific protein out of the whole genomic DNA of S.cerevisiae, with primers wich contain overhanging recognition sites for EcoRI and NheI, and clone it into an his-tag expression vector. What currently confuses me is that these restriction enzymes appear to be able to mess up the whole genomic DNA, or are their recognition sites also methylated in S.cerevisiae ?
So if I don't want to get the whole DNA cut in a thousand parts, am I supposed to only use enzymes, which occur in yeast naturally, or are there better solutions than that?

Thanks in advance

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